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    If , obtain and simplify f(r+1)-f(r).


    Hence, find .
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    What have you tried?
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    (Original post by cucumberpj)
    ...
    Are you studying this material as an independent candidate - you seem to be struggling with a wide range of questions so I am wondering if you have actually been taught any of this
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    f(r+1)-f(r)




    then how to find the summation?
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    (Original post by TenOfThem)
    Are you studying this material as an independent candidate - you seem to be struggling with a wide range of questions so I am wondering if you have actually been taught any of this
    I learnt these all under sequences and series.
    These questions seemed tricky for me.
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    (Original post by cucumberpj)
    I learnt these all under sequences and series.
    These questions seemed tricky for me.
    They are
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    (Original post by TenOfThem)
    They are
    So I hope I can seek help from you all.
    I am doing these in limited sources.
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    (Original post by cucumberpj)
    So I hope I can seek help from you all.
    I am doing these in limited sources.
    Try doing it yourself for a few small values of n to see what is happening. There should be a lot of cancelling so if you are doing big calculations you've gone wrong.
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    (Original post by cucumberpj)





    f(r+1)-f(r)




    then how to find the summation?
    Once you've done that bit, you can immediately write down:

    \displaystyle \sum_{r=1}^n [f(r+1) - f(r)] = -2\sum_{r=1}^n \dfrac{1}{r(r+1)(r+2)}

    The bit on the right is -2 x the sum you're asked to find, and the bit on the left simplifies enormously - try writing it out for a few values of n if you can't see what's going on!
 
 
 
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